Search

This paper introduces the Golf Sport Inspired Search (GSIS) algorithm as an evolutionary search method for numerical optimization. Each solution is generated with the aid of the step-length and search direction. The step-length is determined with the aid of the Tait's model of the trajectory of the golf ball, which is a physical model. The search direction is from the current position in the search space toward the position of a different individual or its reflected position. Such a direction determines the movement direction in the optimization process. A crossover operator is introduced to increase exploration at the starting and exploitation at the ending stages of the search. Performance of the GSIS is compared with many algorithms on 23 + 14 unconstrained classic functions, 29 functions of CEC 2017 benchmark suite and six constrained engineering design problems. Experiments indicate that with the aid of its cleverly designed operators, GSIS is able to produce promising results. Besides a cooperative game theoretic approach is introduced, which is able to measure the effectiveness of different operators in reducing the search cost. Such an approach can be used to measure the effectiveness of different operators that an evolutionary or swarm-intelligence algorithm owns. [ABSTRACT FROM AUTHOR]

This paper presents an effective approach for solving economic load dispatch problems contemplating the scheduling a set of thermal generating units to produce a specific power at low consumption costs. These problems can be thought of as nonlinear, non-convex, and highly constrained optimization problems with a large number of local minima. To cope with the above issues in solving such problems, a new meta-heuristic named capuchin search algorithm was adopted. To boost the search performance of this algorithm as well as to mitigate its early convergence and regression to the local optimum, it was hybridized with another algorithm and improved using several positive amendments. First, a memory element was added to this algorithm to ameliorate its position and velocity update mechanisms in order to exploit the most encouraging candidate solutions. Second, two adaptive parametric functions were used to manage the exploration and exploitation features of this algorithm and balance them appropriately. Finally, the hybridization was made using the gradient-based optimizer to strengthen the intensification ability of this algorithm and balance its searching ability to fulfill sensible search performance. The proficiency of the proposed algorithm was divulged by assessing it on computationally difficult economic load dispatch problems under 6 different tests with a generator of 3, 13, 40, 80, and 140 units, each with different constraints and load conditions. The proposed algorithm provided the best performance among many other competitors. Its superiority and practicality were revealed by obtaining optimal solutions for large-scale test cases such as 40-unit and 140-unit test systems. [ABSTRACT FROM AUTHOR]

Due to the users' mobility, new online applications, as well as low processing power and limited energy of smart devices, traditional cloud computing models could not provide new required services. Cloud service providers improve the quality of their services by moving some servers to the edge of the network and closer to mobile users. Considering the moving nature of users and the heterogeneous service demands in different areas, the optimal placement of servers plays an important role in increasing the quality of service provided to users. However, because of the large number of servers, finding the optimal location of these resources is a serious challenge. In the proposed method of this paper (MES-WG), in the first step, the geographical area of server deployment is divided into smaller sub-regions to reduce the complexity of the problem. Then, by using the WOA algorithm the search agent finds the optimal location of the servers. In the next step, a neural network is used for the local placement of all servers in each area. Finally, game theory is deployed for the convergence of resource placement in all sub-regions. The experimental results show that the proposed method reduces the network latency by 33.5% and also improves the load balance on servers by 28.2%, compared to some of the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Cooperation search algorithm (CSA) is a new metaheuristic algorithm inspired from the team cooperation behaviors in modern enterprises and is characterized by fast convergence. However, for complex multimodal problems, it may get trapped into local optima and suffer from premature convergence for the shortcoming of population updating guided only by leading individuals. In this paper, the issue of low convergence efficiency and convergence accuracy of the CSA algorithm on complex multimodal problems is dramatically alleviated by integrating the mutation and crossover operators in DE algorithm. Experimental results demonstrate the better performance of CCSA on convergence speed and accuracy as compared to other existing optimizers. Furthermore, aiming at the problem that there is no universal approach for the multi-degree reduction in Ball Bézier surfaces under different interpolation constrains, we propose a new method to solve this problem by introducing metaheuristic methods, where the change of interpolation constrains is treated as the change of decision variables. The modeling examples show that the proposed method is effective and easy to implement under different interpolation constrains, which can achieve the multi-degree reduction in Ball Bézier surfaces at one time and can simplify the degree reduction procedure significantly. [ABSTRACT FROM AUTHOR]

Community detection is a prominent research topic in Complex Network Analysis, and it constitutes an important research field on all those areas where complex networks represent a powerful interpretation tool for describing and understanding systems involved in neuroscience, biology, social science, economy, and many others. A challenging approach to uncover the community structure in complex network, and then revealing the internal organization of nodes, is Modularity optimization. In this research paper, we present an immune optimization algorithm (opt-IA) developed to detect community structures, with the main aim to maximize the modularity produced by the discovered communities. In order to assess the performance of opt-IA, we compared it with an overall of 20 heuristics and metaheuristics, among which one Hyper-Heuristic method, using social and biological complex networks as data set. Unlike these algorithms, opt-IA is entirely based on a fully random search process, which in turn is combined with purely stochastic operators. According to the obtained outcomes, opt-IA shows strictly better performances than almost all heuristics and metaheuristics to which it was compared; whilst it turns out to be comparable with the Hyper-Heuristic method. Overall, it can be claimed that opt-IA, even if driven by a purely random process, proves to be reliable and with efficient performance. Furthermore, to prove the latter claim, a sensitivity analysis of the functionality was conducted, using the classic metrics NMI, ARI and NVI. [ABSTRACT FROM AUTHOR]

To overcome the shortcomings of the traditional parameter identification methods of photovoltaic cell model, including low accuracy, slow convergence speed, easy to be trapped in local optimum so on, a parameter identification method of photovoltaic cell model based on improved elephant herding optimization algorithm is proposed in this paper. The fast-moving operator is used, which greatly improves the convergence speed and global searching ability of the algorithm. The elitist strategy is also introduced where the worst individual is replaced with the optimal individual to improve the convergence speed and shorten the optimization time of the algorithm. When applied to the parameter identification of the photovoltaic cell model, the identification result of the improved elephant herding optimization algorithm proves to be better than other algorithms. The parameter identification of the photovoltaic cell model under different radiation conditions is carried out, and the fitting result of identification data is highly consistent with the measured data. Experiments validate that the improved elephant herding optimization algorithm can accurately and effectively identify the parameters of the photovoltaic cell model in different environments. [ABSTRACT FROM AUTHOR]

Over the last decade, the size and complexity of real-world problems have grown dramatically, necessitating more effective tools. Nature-inspired metaheuristic algorithms have proven to be a promising tool for solving such problems due to their performance in a variety of fields. JAYA algorithm is a novel population-based algorithm which could have been able to present reliable results. This is because it does not need any parameters to be set other than the population size and the maximum number of iteration. Despite its positive feedbacks, this algorithm should be modified to witness more efficiency. This paper aims to amend the original version of Jaya to present a high-efficiency version named Powerful Enhanced Jaya (PEJAYA). In other words, the methodology of updating position in Jaya is modified to enhance the convergence and search capabilities. This approach is assessed according to solve 20 well-known benchmark functions, feature selection, and statistical tests. The output results of proposed optimization algorithm are then evaluated by comparing it with other recent algorithms including crow search algorithm (CSA), standard version of JAYA, particle swarm optimization (PSO), dragonfly algorithm (DA), grasshopper optimization algorithm (GOA), moth-flame optimization (MFO) and sine–cosine algorithm (SCA). Solving a real-world problem is another way of checking the efficiency of this approach with other published works. Prompt escape from local minima, superior convergence, and stability demonstrate that the suggested approach is a very powerful instrument that may be employed in a variety of optimization situations. [ABSTRACT FROM AUTHOR]

In the recent years, the optimization problems show that they are a big challenge for engineering regarding the fast growth of new nature-inspired optimization algorithms. Therefore, this paper presents a novel nature-inspired meta-heuristic algorithm for optimization which is called as bear smell search algorithm (BSSA) that takes into account the powerful global and local search operators. The proposed algorithm imitates both dynamic behaviors of bear based on sense of smell mechanism and the way bear moves in the search of food in thousand miles farther. Among all animals, bears have inconceivable sense of smell due to their huge olfactory bulbs that manage the sense of different odors. Since the olfactory bulb is a neural model of the vertebrate forebrain, it can make a strong exploration and exploitation for optimization. According to the odors value, bear moves the next location. Therefore, this paper mathematically models these structures. To demonstrate and evaluate the BSSA ability, numerous types of benchmark functions and four engineering problems are employed to compare the obtained results of BSSA with other available optimization methods with several analyzed indices such as pair-wise test, Wilcoxon rank and statistical analysis. The numerical results revealed that proposed BSSA presents competitive and greater results compared to other optimization algorithms. [ABSTRACT FROM AUTHOR]

This paper introduces a new optimization algorithm called electron radar search algorithm (ERSA) inspired by the electron discharge mechanism. It is based on the natural phenomenon of electric flow as the form of electron discharge through a gas, liquid, or solid environment. When the voltage between separated electrodes (anode and cathode) increases, electrons tendency to emission from a low potential state to the higher potential condition is grown up. However, electrons are trying to find the best path with the least resistance in the medium. At each point, electrons evaluate the surrounding environment with a radar mechanism and least resistance path is selected for the next move. Hence, in this paper, a novel developed meta-heuristic algorithm based on the electrons' search approach is presented and the algorithm is benchmarked on 20 mathematical functions with four well-known methods for validation and verification tests. Moreover, the algorithm is implemented in two engineering design problems (tension/expression spring and welded beam design optimization) and the results demonstrate that the ERSA performs more efficiently for solving unknown search spaces and the algorithm found best solution in approximately 95% of the reviewed benchmark functions. [ABSTRACT FROM AUTHOR]

Parameter-free algorithms are of an increasing interest in applications that require out-of-the-box solving techniques. For instance, scheduling in volatile environments or control parameters optimisation often requires flexible solving approaches without the need to tune or retune the parameters. In addition, parameter-free algorithms are usually beneficial in solving previously unexplored real-world problem instances. In this paper, we propose a parameter-free local search strategy to solve graph colouring, which is the underlying problem for a number of scheduling applications. Two variants of parameter-free local search are computationally investigated: PFLS-A and PFLS-B. Both of these algorithms are based on accepting strictly improving moves and operating as a random walk if no strictly improving move is found. PFLS-A and PFLS-B differ in randomised versus systematic exploration of the neighbourhood of the current solution. Their cooperative variant CPFLS is also proposed. We compare the results of these three algorithms to the results obtained by 13 other local search methods from the literature. CPFLS provides better or equal results as the other local search algorithms in 67.25 % of per-instance comparisons. This is without employing any explicit or implicit parameters that are usually used in metaheuristics. This hints the promising nature of parameter-free metaheuristics not only for this problem but also metaheuristics in general. [ABSTRACT FROM AUTHOR]

One of the most common tasks of groundwater engineers is to estimate aquifer parameters from transient time-drawdown data which are measured during the execution of pumping tests. The classical method consists in the manual superimposition of the observed time-drawdown data over a type-curve, and the appreciation of the goodness-of-fit is left to the visual inspection of the engineer. The present paper proposes a computerized method based on a new hybrid algorithm named CSARao-1. It combines two recent metaheuristic algorithms: the crow search algorithm (CSA) and Rao-1 algorithm for the optimal aquifer parameters estimation, which inherits the advantages of both algorithms. The CSARao-1 hybrid algorithm along with CSA and Rao-1 algorithm was applied in conjunction with both the Theis solution to analyze time-drawdown datasets coming from confined aquifers systems and the Hantush and Jacob solution to analyze datasets coming from leaky aquifers systems. The proposed approach was coded in FORTRAN programming language and evaluated on fourteen time-drawdown datasets coming from different confined and leaky aquifers systems. The results obtained using CSARao-1 hybrid algorithm were compared to those obtained by applying CSA and Rao-1 algorithm separately, and to those recently published. Globally, the proposed CSARao-1 hybrid algorithm was found to exhibit more accuracy, better robustness and higher rate of convergence over the analyzed transient time-drawdown datasets. [ABSTRACT FROM AUTHOR]

Power loss reduction is a very important problem in operating the distribution network. This paper presents a method relied on artificial ecosystem-based optimization (AEO) for the network reconfiguration (NR) problem. The considered goal of the NR problem is to reduce power loss. The performance of the proposed AEO method is evaluated on the 14-node, 69-node and 136-node distribution networks. In addition, the NR approach relied on cuckoo search algorithm (CSA) is also implemented to compare with the proposed AEO method. The statistics result comparisons between AEO and CSA demonstrate that AEO outperforms CSA method with the higher success rate and better quality of the obtained solution in finding the optimal network configuration. In addition, AEO is also better than some previous approaches in the literature in term of the obtained network configuration. Consequently, AEO method is a very effective approach for the NR problem. [ABSTRACT FROM AUTHOR]

In recent decades, researches on optimizing the parameter of the artificial neural network (ANN) model has attracted significant attention from researchers. Hybridization of superior algorithms helps improving optimization performance and capable of solving complex applications. As a traditional gradient-based learning algorithm, ANN suffers from a slow learning rate and is easily trapped in local minima when training techniques such as gradient descent (GD) and back-propagation (BP) algorithm are used. The characteristics of randomization and selection of the best or near-optimal solution of metaheuristic algorithm provide an effective and robust solution; therefore, it has always been used in training of ANN to improve and overcome the above problems. New metaheuristic algorithms are proposed every year. Therefore, the review of its latest developments is essential. This article attempts to summarize the metaheuristic algorithms which have been proposed from the year 1975 to 2020 from various journals, conferences, technical papers, and books. The comparison of the popularity of the metaheuristic algorithm is presented in two time frames, such as algorithms proposed in the recent 20 years and those proposed earlier. Then, some of the popular metaheuristic algorithms and their working principle are reviewed. This article further categorizes the latest metaheuristic search algorithm in the literature to indicate their efficiency in training ANN for various industry applications. More and more researchers tend to develop new hybrid optimization tools by combining two or more metaheuristic algorithms to optimize the training parameters of ANN. Generally, the algorithm's optimal performance must be able to achieve a fine balance of their exploration and exploitation characteristics. Hence, this article tries to compare and summarize the properties of various metaheuristic algorithms in terms of their convergence rate and the ability to avoid the local minima. This information is useful for researchers working on algorithm hybridization by providing a good understanding of the convergence rate and the ability to find a global optimum. [ABSTRACT FROM AUTHOR]

Meta-heuristic algorithms have shown promising results in solving various optimization problems. The crow search algorithm (CSA) is a new and effective meta-heuristic algorithm that emulates crows' intelligent group behavior in nature. However, it suffers from several problems, such as trapping into local optimum and premature convergence. This paper proposes an improved crow search algorithm (ICSA), which has been tested and evaluated by a set of well-known benchmark functions. A new update mechanism that uses the merits of the global best position to move toward the best position is proposed. This mechanism increases the convergence of the algorithm and improves its local search-ability. Twenty benchmark functions are used to evaluate the performance of the proposed ICSA. Moreover, the ICSA algorithm is compared with the conventional CSA and other meta-heuristic algorithms such as particle swarm optimization (PSO), dragonfly algorithm (DA), grasshopper optimization algorithm (GOA), gray wolf optimizer (GWO), moth-flame optimization (MFO), and sine-cosine algorithm (SCA). The experimental result shows that the proposed ICSA algorithm has produced promising results and outperformed conventional CSA and other meta-heuristic algorithms. Also, the proposed ICSA has a more robust convergence for optimizing objective functions in terms of solution accuracy and efficiency. [ABSTRACT FROM AUTHOR]

In this paper, a cooperative bat searching algorithm (CBA) is proposed by using a communication topology to share information among all the bats in bat algorithm (BA). Inspired by the cooperation mechanism in the distributed control theory, a cooperative term is added to the original BA to accelerate the searching process. The convergence issue is rigorously studied for CBA by using the Jury's test. Moreover, numerical evaluation is conducted to compare CBA with other variants of BA by solving fifteen benchmark functions from IEEE congress on evolutionary computation. The results are provided to demonstrate the effectiveness of the proposed CBA. As an application, CBA and binary CBA are equipped as the real-time optimizers in a networked model predictive control strategy to solve a balanced coordination problem. The proposed CBA showed competitive performance. [ABSTRACT FROM AUTHOR]

In the presented paper, the functioning and the results of the work of two metaheuristic algorithms, namely cuckoo search algorithm (CS) and firefly algorithm (FA), are described using the apparatus of generalized nets (GNs), which is an appropriate and efficient tool for describing the essence of various optimization methods. The two developed GN-models mimic the optimization processes based on the nature of cuckoos and fireflies, respectively. The proposed GN-models execute the two considered metaheuristic algorithms conducting basic steps and performing optimal search. Building upon these two GN-models, a universal GN-model is constructed that can be used for describing and simulating both the CS and the FA by setting different characteristic functions of the GN-tokens. Moreover, the universal GN-model itself can be transformed to each of the herewith presented GN-models by applying appropriate hierarchical operators. In order to validate the proposed universal GN-model, numerical experiments are performed for the operating of the universal GN-model (CS and FA) on benchmark mathematical functions. The obtained results are compared with the results of the GN-model of CS, GN-model of FA, as well as the results of the standard CS and FA. [ABSTRACT FROM AUTHOR]

Stochastic Fractal Search (SFS) is a novel and powerful metaheuristic algorithm. This paper presents a Multi-Objective Stochastic Fractal Search (MOSFS) for the first time, to solve complex multi-objective optimization problems. The presented algorithm uses an external archive to collect efficient Pareto optimal solutions during the optimization process. Using dominance rules, leader selection and grid mechanisms, MOSFS precisely approximates the true Pareto optimal front. The MOSFS is implemented on nine multi-objective benchmark functions (CEC 2009) with multimodal, convex, discrete and non-convex optimal Pareto fronts. Performance of the proposed algorithm is compared to well-known algorithms. In addition, different performance measures are considered to evaluate the convergence and coverage abilities of the algorithms including Inverted Generational Distance, Maximum Spread and Spacing. Furthermore, statistical analyses are utilized to determine the superior algorithm. The results revealed that the MOSFS performs significantly better than other algorithms in both convergence and coverage and it is able to approximate true Pareto front precisely. In the end, MOSFS is implemented to solve a real-world engineering design problem called welded beam design problem and efficiency of the algorithm is compared to recently developed algorithms. The results of simulations and the Wilcoxon rank-sum test showed that the MOSFS is able to provide the most promising Pareto front for the problem considering various performance metrics at a 95% confidence level. [ABSTRACT FROM AUTHOR]

Bat algorithm (BA) is a powerful nature-inspired swarm algorithm which finds applicability to a diverse range of problem domains. Though it is efficient, it suffers from two handicaps: possibility of being trapped in local optima and lost convergence speed as the algorithm progresses. This paper proposes swarm bat algorithm with improved search (SBAIS). SBAIS gains superior exploration capabilities by employing swarming characteristics inspired by shuffled complex evolution (SCE) algorithm. Best bats of the population are kept in a super-swarm, while all other bats are partitioned according to SCE. The super-swarm uses the search mechanism of bat algorithm with improved search to perform refined search around the best solution, which makes sure that the convergence speed of the algorithm is not lost. Every other swarm gets one solution from the super-swarm before starting their evolution process. These swarms evolve using standard bat algorithm, helping the algorithm to escape any possible local optima. SBAIS further keeps a check on the overall diversity of the population. If the diversity drops below a given threshold value, new random solutions are added to the population. Performance of SBAIS is validated by comparing it to BA and fourteen recent variants of bat algorithm over 30 standard benchmark optimization functions, CEC'05 and CEC'14 function sets. Results established the superiority of SBAIS over the compared algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a novel meta-heuristic search algorithm inspired by rhinoceros’ natural behaviour is proposed, namely rhinoceros search algorithm (RSA). Similar to our earlier version called elephant search algorithm, RSA simplifies certain habitual characteristics of rhinoceros and stream-lines the search operations, thereby reducing the number of operational parameters required to configure the model. Via computer simulation, it is shown that RSA is able to outperform certain classical meta-heuristic algorithms. Different dimensions of optimization problems are tested, and good results are observed by RSA. The RSA is also implemented on permutation flow-shop scheduling problem (PFSP) with some representation method. Four different problem scales are used. Compared with partible swarm optimization (PSO) on PFSP, the RSA outperforms PSO on different problem scales with a 3% improvement. [ABSTRACT FROM AUTHOR]

Data clustering is one of the most popular branches of machine learning and data analysis. Partitioning-based type of clustering algorithms, such as K-means, is prone to the problem of producing a set of clusters that is far from perfect due to its probabilistic nature. The clustering process starts with some random partitions at the beginning, and then it attempts to improve the partitions progressively. Different initial partitions can result in different final clusters. Trying through all the possible candidate clusters for the perfect result is computationally expensive. Meta-heuristic algorithm aims to search for global optimum in high-dimensional problems. Meta-heuristic algorithm has been successfully implemented on data clustering problems seeking a near optimal solution in terms of quality of the resultant clusters. In this paper, a new meta-heuristic search method named elephant search algorithm (ESA) is proposed to integrate into K-means, forming a new data clustering algorithm, namely C-ESA. The advantage of C-ESA is its dual features of (i) evolutionary operations and (ii) balance of local intensification and global exploration. The results by C-ESA are compared with classical clustering algorithms including K-means, DBSCAN, and GMM-EM. C-ESA is shown to outperform the other algorithms in terms of clustering accuracy via a computer simulation. C-ESA is also implemented on time series clustering compared with classical algorithms K-means, Fuzzy C-means and classical meta-heuristic algorithm PSO. C-ESA outperforms the other algorithms in term of clustering accuracy. C-ESA is still comparable compared with state of art time series clustering algorithm K-shape. [ABSTRACT FROM AUTHOR]

This paper deals with the pollution-routing problem with simultaneous pickup and delivery, where the goal is to minimize fuel consumption and emissions by scheduling and routing customers. A nonlinear mix integer programing model is presented for this problem, and an adaptive large neighborhood search heuristic is proposed for the solution method including new removal and insertion operators. Also a heuristic algorithm is proposed to construct the initial solution. The proposed method is validated by computational experiments conducted on two classes of benchmark instances. The experiments further show that our proposed heuristic outperforms related heuristics and improved the results of existing literature. [ABSTRACT FROM AUTHOR]

Nowadays, wireless sensor networks (WSNs) are considered in many fields of application. In this paper, we study how to efficiently deploy relay nodes into previously established static WSNs, with the purpose of optimising two relevant factors for the industry: average energy consumption of the sensors and average sensitivity area provided by the network. This is the so-called relay node placement problem, which is a known NP-hard optimisation problem in the literature. With the purpose of tackling this multiobjective (MO) optimisation problem, we consider two different approaches of the trajectory algorithm MO-VNS, assuming a wide range of stop conditions. Two additional standard genetic algorithms are included in this study, NSGA-II and SPEA2, which belong to evolutionary algorithms. The aim is to analyse the behaviour of MO-VNS compared to traditional methodologies. To this end, the four metaheuristics are applied to solve a freely available data set. The results obtained are analysed following a widely accepted statistical methodology and considering three MO quality metrics: hypervolume, set coverage, and attainment surface. After studying the results, we conclude that MO-VNS provides better performance than the standard algorithms NSGA-II and SPEA2. Moreover, we verify that the addition of relay nodes is a good way to optimise traditional WSNs. [ABSTRACT FROM AUTHOR]

Clustering is a popular data analysis technique, which is applied for partitioning of datasets. The aim of clustering is to arrange the data items into clusters based on the values of their attributes. Magnetic charge system search (MCSS) algorithm is a new meta-heuristic optimization algorithm inspired by the electromagnetic theory. It has been proved better than other meta-heuristics. This paper presents a new hybrid meta-heuristic algorithm by combining both MCSS and particle swarm optimization (PSO) algorithms, which is called MCSS-PSO, for partitional clustering problem. Moreover, a neighborhood search strategy is also incorporated in this algorithm to generate more promising solutions. The performance of the proposed MCSS-PSO algorithm is tested on several benchmark datasets and its performance is compared with already existing clustering algorithms such as K-means, PSO, genetic algorithm, ant colony optimization, charge system search, chaotic charge system search algorithm, and some PSO variants. From the experimental results, it can be seen that performance of the proposed algorithm is better than the other algorithms being compared and it can be effectively used for partitional clustering problem. [ABSTRACT FROM AUTHOR]

Run-time analysis is a method that characterizes the run-time behaviour of an algorithm. It has been successfully used to analyse metaheuristics and stochastic local search algorithms. Some studies on genetic programming and related stochastic search algorithms suggested the existence of a rationale behind the run-time behaviour which could be exploited to better understand the algorithm looking at its run-time response. Under that hypothesis, this paper presents empirical evidence suggesting common statistical properties in the run-time of several types of population-based search algorithms, including genetic algorithms, genetic programming, grammatical evolution, differential evolution or particle swarm optimization. In this analysis, only the run-time of runs that were able to find a solution are considered; unsuccessful runs are not included in the analysis. The run-time to find a solution, measured by the number of evaluations, of some well-known evolutionary algorithms is empirically obtained, finding that it usually can be approximated using a lognormal distribution, with the exception of some difficult problems, which are better approximated by an exponential. We also show that the algorithm parameter settings might influence the yielding run-time statistical distribution; in particular, when there is no selective pressure, the run-time, measured as the number of evaluations to find a solution, follows a Weibull distribution instead of a lognormal one. Finally, we outline a framework using a simple theoretical discrete-time model, showing that the geometrically distributed run-time is a consequence of the lack of memory in the algorithm. [ABSTRACT FROM AUTHOR]

Scatter search (SS) is a metaheuristic framework that explores solution spaces by evolving a set of reference points. These points (solutions) are initially generated with a diversification method and the evolution of these reference points is induced by the application of four methods: subset generation, combination, improvement and update. In this paper, we consider the application of the SS algorithm to the unconstrained global optimization problem and study its performance when coupled with different improvement methods. Specifically, we design and implement new procedures that result by combining SS with eight different improvement methods. We also propose an SS procedure (on the space of parameters) to determine the values of the key search parameters used to create the combined methods. We finally study whether improvement methods of different quality have a direct effect on the performance of the SS procedure, and whether this effect varies depending on attributes of the function that is minimized. Our experimental study reveals that the improvement method is a key element in an effective SS method for global optimization, and finds that the best improvement methods for high-dimensional functions are the coordinate method and two versions of scatter search itself. More significantly, extensive computational tests conducted with 12 leading methods from the literature show that our resulting method outperforms competing methods in the quality of both average solutions and best solutions obtained. [ABSTRACT FROM AUTHOR]